Blender 2.8 Copy 50% bone rotation between different local axis
If the orientation of a bone is not correct you can change it in Edit mode with ctrlR (manual), or ShiftN (automatic). To display the axis go in the Properties panel > Object Data > Viewport Display > Axes.



Now if you want a bone to influence the rotation of another bone, in Pose mode, you can give the second bone a Copy Rotation constraint (in my case Space: Local Space - Local Space) and reduce the influence value to 50% if it needs to.



If you want the second bone to copy the rotation of the first one, but on a different axis, use a Copy Transformation constraint. For example here I want bone2's Y axis rotation to copy bone1's X axis rotation. I need to set all the values properly.